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# Solving One-Variable Equations

## Objective

Solve and graph inequalities with variables on both sides of the inequality.

## Common Core Standards

### Core Standards

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• A.REI.B.3 — Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

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• 7.EE.B.4.B

## Criteria for Success

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1. Solve inequalities with variables on both sides and use substitution to check answers.
2. Accurately multiply and divide with negative coefficients in inequalities, paying close attention to the direction of the inequality symbol.
3. Graph solutions to inequalities.
4. Write, solve, and interpret solutions to inequalities for applications.

## Tips for Teachers

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Lessons 11 and 12 extend on 7.EE.4b and bridge a gap to high school standard A.REI.3. Inequalities are not included in the 8th grade standards, but this is a natural extension of students’ work with equations from earlier in the unit, especially now that students are able to work with more complex equations and inequalities. These two lessons can be treated as optional.

#### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problems 2 and 3 (benefit from worked examples). Note, this is beyond 8th grade expectations, bridging a gap between 7th grade and HS; this lesson may be skipped. Find more guidance on adapting our math curriculum for remote learning here.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

## Anchor Problems

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### Problem 1

Solve the inequality. Then pick a value for $x$ and check your answer. Lastly, graph your solution on a number line.

$7-{2\over3}x>2+x$

### Problem 2

Solve the inequality.

${\frac{x-7}{3}\leq \frac{2(x-1)}{8}}$

### Problem 3

Lindsay and Kiana work at the same restaurant. Lindsay earns $12.75 per hour and Kiana, who has been working there longer, earns$15.25 per hour. One week, both girls work the same number of hours at the restaurant, but Lindsay spends $37 and Kiana spends$55. At the end of the week, Lindsay has more money left than Kiana. What is the smallest number of hours the girls could have worked for this to be true?

## Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

• Include problems that cover all types of equations and inequalities.
• Include application problems that cover all types of equations and inequalities; students determine if an equation or inequality best represents the situation.
• Kuta Software Free Algebra 1 Worksheets InequalitiesMulti-Step Inequalities (Use inequalities with variables on both sides.)
• Kuta Software Free Pre-Algebra Worksheets InequalitiesMulti-Step Inequalities (Use inequalities with variables on both sides.)

${\frac{-2x+1}{4}< \frac{3x-6}{6}}$